Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 360, 280, 285 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 360, 280, 285 is 5 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 360, 280, 285 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 360, 280, 285 is 5.
HCF(360, 280, 285) = 5
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 360, 280, 285 is 5.
Step 1: Since 360 > 280, we apply the division lemma to 360 and 280, to get
360 = 280 x 1 + 80
Step 2: Since the reminder 280 ≠ 0, we apply division lemma to 80 and 280, to get
280 = 80 x 3 + 40
Step 3: We consider the new divisor 80 and the new remainder 40, and apply the division lemma to get
80 = 40 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 40, the HCF of 360 and 280 is 40
Notice that 40 = HCF(80,40) = HCF(280,80) = HCF(360,280) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 285 > 40, we apply the division lemma to 285 and 40, to get
285 = 40 x 7 + 5
Step 2: Since the reminder 40 ≠ 0, we apply division lemma to 5 and 40, to get
40 = 5 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 40 and 285 is 5
Notice that 5 = HCF(40,5) = HCF(285,40) .
Here are some samples of HCF using Euclid's Algorithm calculations.
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 360, 280, 285?
Answer: HCF of 360, 280, 285 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 360, 280, 285 using Euclid's Algorithm?
Answer: For arbitrary numbers 360, 280, 285 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.